Holographic theories at finite θ-angle, CP-violation, glueball spectra and strong-coupling instabilities

A general class of holographic theories with a nontrivial θ-angle are analyzed. The instanton density operator is dual to a bulk axion field. We calculate the ground-state solutions with nontrivial source, a${}_{UV}$, for the axion, for both steep and soft dilaton potentials in the IR, and both in d = 3 and d = 4. We find all cases to be qualitatively similar. We also calculate the spin=2, 0 glueball spectra and show that the glueball masses monotonically decrease as functions of a${}_{UV}$ (or θ-angle). The slopes of glueball masses are different, generically, in different potentials. In the case of steep dilaton potentials, the glueball (masses)${}^2$ turn negative before the maximum of a${}_{UV}$is attained. We interpret this as a signal for a favored instanton condensation in the bulk. We also investigate strong CP-violation in the effective glueball action. (© 2020 Wiley‐VCH GmbH)